OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 3 — Mar. 1, 2010
  • pp: 599–604

Perturbed multilayered structures of positive and negative index materials

R. Aylo, P. P. Banerjee, and G. Nehmetallah  »View Author Affiliations

JOSA B, Vol. 27, Issue 3, pp. 599-604 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (599 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this work, we study the influence of disorder on the omnidirectional bandgap in a one dimensional stack of alternating positive and dispersive negative index materials. We achieve this through using the transfer matrix method to study wave propagation properties. In the case where the number of periods becomes infinitely large, the limit of the transmittance is derived from the trace of the matrix, and thus reducing the calculation complexity. The origin of the transmission resonances and their relation with the field localization for random systems are analyzed and compared with that of the periodic case. Our result shows that the zero average refractive index bandgap is not affected by small disorders in layer thickness or refractive index, and thus the multilayer stack is robust against fabrication. The finding is expected to achieve potential applications in optoelectronic sensor devices such as omnidirectional reflectors in airplane radomes. We also show that a random mixture of positive and dispersive negative index materials in an equal ratio always possesses a zero average refractive index bandgap.

© 2010 Optical Society of America

OCIS Codes
(160.3918) Materials : Metamaterials
(310.4165) Thin films : Multilayer design
(260.2710) Physical optics : Inhomogeneous optical media

ToC Category:

Original Manuscript: December 14, 2009
Manuscript Accepted: January 11, 2010
Published: February 26, 2010

R. Aylo, P. P. Banerjee, and G. Nehmetallah, "Perturbed multilayered structures of positive and negative index materials," J. Opt. Soc. Am. B 27, 599-604 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  2. V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968). [CrossRef]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000). [CrossRef] [PubMed]
  4. R. Aylo, P. P. Banerjee, and G. Nehmetallah, “ Perturbation of multilayered structures of positive and negative index materials,” Proc. SPIE 7392, 7392Q1 (2009).
  5. R. Aylo, P. P. Banerjee, and G. Nehmetallah, “Optical propagation through a homogeneous mixture of positive and negative index materials,” Proc. SPIE 7029, 702917 (2008). [CrossRef]
  6. H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative index materials,” Appl. Phys. Lett. 83, 5386-5438 (2003). [CrossRef]
  7. J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003). [CrossRef] [PubMed]
  8. Y. Yuan, L. Ran, J. Huangfu, and H. Chen, “Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials,” Opt. Express 14, 2220-2227 (2006). [CrossRef] [PubMed]
  9. P. Han, C. T. Chan, and Z. Q. Zhang, “Wave localization in one-dimensional random structures composed of single-negative metamaterials,” Phys. Rev. B 77, 115332 (2008). [CrossRef]
  10. Y. Weng, Z. Wang, and H. Chen, “Band structures of 1D wavelength photonic crystals containing metamaterials,” Phys. Rev. E 75, 046601 (2007). [CrossRef]
  11. W. H. Sun, Y. Lu, R. Peng, L. Bao, D. Li, X. Wu, and M. Wang, “Omnidirectional transparency induced by matched impedance in disordered metamaterials,” J. Appl. Phys. 106, 013104 (2009). [CrossRef]
  12. A. A. Asatryan, L. C. Botten, M. Byrne, V. Freilkher, S. Gredeskul, I. V. Shardrivov, R. C. McPhedran, and Y. Kishvar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007). [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  14. H. A. Macleod, Thin Film Optical filters (Taylor & Francis, 2001). [CrossRef]
  15. J. Lekner, “Light in periodically stratified media,” J. Opt. Soc. Am. A 11, 2892-2899 (1994). [CrossRef]
  16. Y. Dong and X. Zhang, “Unusual transmission properties of wave in one-dimensional random system containing left-handed material,” Phys. Lett. A 359, 542-546 (2006). [CrossRef]
  17. D. Felbacq and B. Guizal, “Limit analysis of the diffraction of a plane wave by a one-dimensional periodic medium,” J. Math. Phys. 39, 4604-4607 (1998). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited